This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

A window frame in Salt's Mill consists of two equal semicircles and a circle inside a large semicircle. What is the radius of the circle?

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

How many trains can you make which are the same length as Matt's, using rods that are identical?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.

Can you find any two-digit numbers that satisfy all of these statements?

Can you find any two-digit numbers that satisfy all of these statements?

How many routes are there in this diagram from S to T?

You and your friends are probably quite good at imagining things and seeing things in lots of different ways. Here you'll put that to use in doing some maths challenges.

You and your friends are probably quite good at imagining things and seeing things in lots of different ways. Here you'll put that to use in doing some maths challenges.

Without scale and measurement, science, design and engineering would not exist!

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

These five clowns work in pairs. What is the same and what is different about each pair's faces?

are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures. This problem considers the eight semi-regular tessellations which pose a demanding challenge in terms of. . . .

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

How many possible necklaces can you find? And how do you know you've found them all?

Why might you wish to study science at university? Read about the views of current students! UNDER DEVELOPMENT

Can you sketch these difficult curves, which have uses in mathematical modelling?

A selection of interesting mathematics challenges which pave the way to the applied mathematics of greatest use at university.

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

Try the Chinese version of this well-known game with a friend. Great to play in the garden or in the park.

When waiting for a ride on outdoor toys, children can consider which route they might take around the outside area and how long they will spend on their toy.

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?